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Application of sparse dictionary learning to seismic data reconstruction
HAMID REZA KHATAMI1 ,
MOHAMMAD ALI RIAHI2 ,
MOHAMMAD MAHDI ABEDI3
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1
Petroleum, Mining and Materials Engineering, Islamic Azad University, Central Tehran Branch, Tehran, Iran.,
2
Institute of Geophysics, University of Tehran, Tehran, Iran.,
3
BCAM - Basque Center for Applied Mathematics, Bilbao, Spain.,
JSE 2023, 32(2), 185–204;
Submitted: 11 January 2023 | Accepted: 15 March 2023 | Published: 1 April 2023
© 2023 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Khatami, H.R., Riahi, M.A. and Abedi, M.M., 2023. Application of sparse dictionary learning to seismic data reconstruction. Journal of Seismic Exploration, 32:185-204. According to the principle of compressed sensing (CS), under-sampled seismic data can be interpolated when the data becomes sparse in a transform domain. To sparsify the data, dictionary learning presents a data-driven approach trained to be optimized for each target dataset. This study presents an interpolation method for seismic data in which dictionary learning is employed to improve the sparsity of data representation using improved Kth Singular Value Decomposition (K-SVD). In this way, the transformation will be highly compatible with the input data, and the data in the converted domain will be sparse. In addition, the sampling matrix is produced with the restricted isometry property (RIP). To reduce the sensitivity of the minimizer term to the outliers, we use the smooth L1 minimizer as a regularization term in the regularized orthogonal matching pursuit (ROMP). We apply the proposed method to both synthetic and real seismic data. The results show that it can successfully reconstruct seismic data.
Keywords
compressed sensing
dictionary learning
optimization
reconstruction
sparsity
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